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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 41342 (02)
- University: Sharif University of Technology
- Department: Mathematical Science
- Advisor(s): Akbari, Saeed
- Abstract:
- A fullerene graph is a cubic and 3-connected plan graph that has exactly 12 faces of size5 and other faces of size 6, which can be regarded as the molecular graph of fullerene.In the irst part of this thesis we study some important deinitions and theorems whichused in the other parts.A matching of a graph G is a set M of edges of G such that no two edges of M sharean end-vertex; further a matching M of G is perfect if any vertex of G is incident with anedge of M. A matching M of G is maximum if |M| ? |N| for any other matching N in G. Amatching M is maximal if it is not a proper subset of some other matching in G. Obviously,any maximum matching in G is also a maximal matching. An interesting quantity is thesmallest possible number of edges in a maximal matching of G. This number is called thesaturation number of G. In the second part of this thesis we investigate some bounds of thenumber of diferent perfect matchings and saturation number of fullerene graphs.In the third part of this thesis we obtain chromatic number, chromatic index and fractionalchromatic index of fullerene graphs In the fourth part of this thesis using of some theorems in linear algebra, we obtainsome bounds for the eigenvalues of fullerene graphs and investigate some methods to ind theeigenvalues of regular polyhedras and some fullerene graphs
- Keywords:
- Fullerene ; Chromatic Number ; Matching ; Eigen Values ; Fullerene Graph ; Saturation Number
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